Notice! Contains spoilers for Superman #21!
Due to the never-ending nature of comics, it's completely reasonable that Superman I wish some of his villains would disappear forever. Some villains like Toy Maker can be truly defeated by reforming them. Other villains like Brainiac could even be substantiated depending on interpretation. Yet, Judgment Day has always been relentless, leaving Superman wishing he could defeat him forever. Now, it seems that the superhero has forgotten that he has already eliminated the threat.
Superman has been fighting Doomsday for decades and has been a consistent threat to the Super-Family. Young Jon Kent even considered Doomsday the family bogeyman. It seems that no matter what Superman does, he can never defeat Doomsday. Judgment Day was killed and sent to Hell, and Judgment Day simply broke out again. Superman trapped Doomsday in an infinite teleportation loop and he managed to escape from that as well.
Superman even attempted to trap Doomsday in the Phantom Zone only for him to explode with pure physical force. Superman laments to Lois Lane in Superman #21 by Joshua Williamson and Dan Mora that he wishes he knew how to defeat Doomsday once and for all so they could get rid of him. The problem is this: Superman defeated Doomsday in 1994 and has apparently completely forgotten about him.
Superman has already found the perfect way to kill Doomsday
Superman/Apocalypse: Hunter/Prey #3 by Dan Jurgens, Brett Breeding, Bill Oakley and Greg Wright.
Superman fought Doomsday quite, and he tried several different ways to kill him. The only successful method was way back Superman/Apocalypse: Hunter/Prey where, after Doomsday utterly destroys Darkseid, Superman uses Waverider's help to bring Doomsday to the end of the universe. After all, at the end of time, the only thing left is entropy. Faced with literal oblivion, Judgment Day is simply erased from existence. Not even the evolution of the Last Judgment can face the end of existence. However, it appears that Superman has completely forgotten he did this.
While it is true that Judgment Day still exists today, this is only due to some very special circumstances. When Superman brought Doomsday to the end of time, he died. The only reason he is still alive today is due to Hal Jordan enacting the Zero Hour Crisis and Brainiac's interference. Using the time disruption caused by Zero Hour, Brainiac was able to rip Doomsday from the timeline immediately after Superman left him at the end of the universe. Presumably, if Superman simply took Doomsday there again, he would finally get rid of the beast. If it worked once, what's to stop the plan from working again?
Superman defeated Doomsday over 20 years ago
Apparently the hero forgot how he did it
Some people might argue that this Superman is a different Superman than the one who killed Doomsday and therefore would not have been aware of the plan. The problem with this assumption is post-New 52 Superman and pre-New 52 Superman were fused during the events of Superman: Reborn by Dan Jurgens and Peter Tomasi. The combination means this Superman should have all the memories of any previous adventures of Superman. Even ignoring this, Infinite Frontier also stated that everything is canonical. This means that the only logical explanation is that Superman simply took one too many hits to the head and totally forgot he killed. Judgment Day already.
Superman #21 It's on sale now at DC Comics!